[dghlsakjg]

If someone can figure out how to cheat on an exam where each answer depends on the previous, and the original seed is unique to each student, wouldn't it show a pretty thorough mastery of the subject matter?

I think the larger point is that it is fairly easy in any subject to design a test that is very hard to cheat on. It is much harder to find the resources in modern education to grade that test since each submission is likely unique.

Tests that are easy to grade (like multiple choice), tend to be tests that are easy to cheat....

[Tainnor]

How do you propose that this should work e.g. in proof-based maths courses? You can't just tweak a theorem to prove by the value of some "unique seed", the theorem might become wrong.

It's true that you usually can't cheat your way through such an exam provided you actually write the answer yourself, but in a take-home situation you can always ask someone else to solve it for you.

[sudosysgen]

You do what my teachers do and have unique problem generation software.

[Tainnor]

what? how does that work?

[sudosysgen]

You give it a few hundred problem classes, and constraints for possible answers, and it will randomize the class of problems and generate a unique problem as well as calculate the answer. Then you submit the answer as well as your work and it gets corrected.

For things such as proofs, it might give you a problem for which the theorem is needed, then ask you to solve the problem, indicate which theorem you used, and then prove the theorem.

[Tainnor]

Do you have any example of any software that can generate problems for actual proof-based courses (e.g. abstract algebra)? I'm having a really hard time imagining this, we can't even fully automate theorem proving - how are we supposed to automate theorem generation? And this ignores the fact that you also need to make sure that all the proofs are "of the same difficulty" in terms of fairness.

[sudosysgen]

Ah, no, the theorems would have to be manually selected. But given a high enough number and an automatically generated context it makes cheating much harder.

[RegnisGnaw]

The problem is COVID. You can’t have a large gathering. So everyone is doing their exam at home.

Please tell me how you would structure such an exam without a proctoring system as described.

[bzbarsky]

One option, if you have a reasonably low student-to-instructor ratio: make it an oral 1-1 exam for each student. A video call with the instructor and the student; you ask questions, they answer. If you have 20-ish students, it will eat up half a work-week or so, which is more work than grading 20 exam papers, but not _that_ much more.

Of course if you have 50 students per instructor this is not going to work...

[dghlsakjg]

It depends on the subject. I studied computer science and econ.

Computer science: Solve a complex problem in code. Include a git history. Be ready to defend your program design if I get suspicious.

Econ: Long answer question: Pick 5 concepts that we learned about that you think are most important. Explain them as you would to a ten year old.